Question: Solve for $x$ and $y$ using elimination. ${6x-6y = 30}$ ${5x+5y = 55}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $6$ ${30x-30y = 150}$ $30x+30y = 330$ Add the top and bottom equations together. $60x = 480$ $\dfrac{60x}{{60}} = \dfrac{480}{{60}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {6x-6y = 30}\thinspace$ to find $y$ ${6}{(8)}{ - 6y = 30}$ $48-6y = 30$ $48{-48} - 6y = 30{-48}$ $-6y = -18$ $\dfrac{-6y}{{-6}} = \dfrac{-18}{{-6}}$ ${y = 3}$ You can also plug ${x = 8}$ into $\thinspace {5x+5y = 55}\thinspace$ and get the same answer for $y$ : ${5}{(8)}{ + 5y = 55}$ ${y = 3}$